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Airbus states that the range of the Beluga XL is 4000 km at maximum payload. Does anyone have a figure (or estimate) for it's maximum range with no payload?

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2 Answers 2

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For an estimate, we can use the Brequet range equation:

$range = V\cdot t_f = \frac{L}{D} \times I_{sp} \times \ln\left(\frac{W_i}{W_f}\right) $

with:

  • $V$: optimal velocity
  • $t_f$: flight time
  • $L$: lift
  • $D$: drag
  • $I_{sp}$: propulsion efficiency
  • $W_i$: initial weight
  • $W_f$: final weight

Assuming the lift to drag ratio $\left(\frac{L}{D}\right)$ and the propulsion efficiency will stay constant, the range will depend on the ratio of initial and final weight.

$range = C \times \ln\left(\frac{W_i}{W_f}\right)$

In case the aircraft departs with the maximum payload, the weight is:

$W_i = W_{oe} + W_{payload} + W_{fuel} = W_{mto}$

  • $W_{oe}$: operating empty weight: 127 500 kgf
  • $W_{payload}$: payload weight: 51 000 kgf
  • $W_{mto}$: maximum take-off weight: 227 000 kgf
  • $W_{fuel}$: fuel weight = $W_{mto} - W_{payload}-W_{oe}$ = 48 500 kgf

The final weight at maximum range is then: $W_f = W_{oe} + W_{payload}$

Filling in the numbers we find:

4000 km = $C \times \ln\left(\frac{\textrm{227 000}}{\textrm{127 500 + 51 000}}\right)$

That means $C \approx \textrm{16 640}$ for the Beluga XL.

If we now remove the payload and take-off with the same amount of fuel, we find:

  • $W_i$ = 176 000 kgf
  • $W_f$ = 127 500 kgf
  • $range \approx \textrm{16 640} \times \ln\left(\frac{\textrm{176 000}}{\textrm{127 500}}\right) \approx 5365$km

But that is just removing the payload without adding fuel. Of course we can now bring more fuel on board without exceeding the maximum take-off weight.

The fuel capacity of the Beluga XL is 73000 kg (source:Aircraft Characteristics Airport And Maintenance Planning Beluga XL manual). This changes the numbers to:

  • $W_i$ = 200 500 kgf
  • $W_f$ = 127 500 kgf
  • $range \approx \textrm{16 640} \times \ln\left(\frac{\textrm{200 500}}{\textrm{127 500}}\right) \approx 7530$km

So the Beluga can fly approximately 7500 km when empty, enough to cross the Atlantic from Toulouse, even if there is normal headwind.

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It can travel 4259 kilometers or 2647 miles loaded, but I am not sure if Airbus would have a need to publicly document the information of the unloaded range - I doubt this information is accessible.

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    $\begingroup$ Why dismiss the case of positioning the aircraft empty? If it takes 3 hops to get from A to B loaded, it may take two legs, or maybe only one, to get from B to A empty. $\endgroup$
    – Ralph J
    Jan 10, 2020 at 21:00

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